A simplified depth-averaged debris flow model with Herschel-Bulkley rheology for tracking density evolution: a finite volume formulation

A two-phase depth-averaged debris flow model simplified by momentum equations is presented to solve the tracking of density evolution and simulate high-velocity impact problems. In the model, the Herschel-Bulkley rheology is used to describe the internal and basal frictions in the debris flow, and the treatments of complex terrains and entrainments are also included. To solve the debris flow model numerically, a relevant finite volume formulation including the Harten-Lax-van Leer-Contact (HLLC) scheme is introduced to solve the conservation equation with a debris interface. A circular dam-break, a dam-break of non-Newtonian fluid, and multiple debris flow cases are carried out based on the proposed model to validate the shock-capturing capability, the numerical isotropy, the model accuracy, and the mass conservation. These results indicate that the implemented schemes can produce sufficient numerical stability and accuracy for the debris flow problem. Finally, the debris flow of various rheological properties is systematically simulated, and how the debris rheology affects debris flow behavior is discussed.